An approach to improve the coherence index-based bound has been proposed in [1]} by analyzing the initial estimate and the support uncertainty principle as in [2]}, [3]}. The approach presented in [1]} guarantees unique reconstruction of a sparse signal using the orthogonal matching pursuit approach. In this paper, a relaxed coherence index condition will be derived for the existence of the unique solution of the compressive sensing problem, using the Gershgorin disk theorem. This result guarantees the unique solution existence, but not its reconstruction, meaning that the obtained bound can be relaxed as compared to the one introduced in [1]}. The new result for the sparsity bound will be related to the classical one and those proposed in [1]}, as well as illustrated on numerical examples.
